Two young mathematicians witness the perils of drinking too much coffee.

We use derivatives to help locate extrema.

Here we’ll practice on maxima and minima concepts.

We use the first derivative to help locate extrema.

Here we’ll practice using the first derivative test.

Here we examine what the second derivative tells us about the geometry of functions.

Here we’ll practice using the second derivative test.

Two young mathematicians discuss how to sketch the graphs of functions.

We use the language of calculus to describe graphs of functions.

Two young mathematicians discuss how to sketch the graphs of functions.

We will give some general guidelines for sketching the plot of a function.

Two young mathematicians discuss optimization from an abstract point of view.

Now we put our optimization skills to work.

Two young mathematicians discuss optimizing aluminum cans.

Now we put our optimization skills to work.

Here we’ll practice solving optimization problems.